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Research Article
A multilevel adaptive solver based on second-generation wavelet thresholding techniques
Article first published online: 2 FEB 2006
DOI: 10.1002/nla.479
Copyright © 2006 John Wiley & Sons, Ltd.
Issue
1099-1506/asset/cover.gif?v=1&s=4c716168b1bef317e4ae1ebaac712130c9fe6913 "Numerical Linear Algebra with Applications")
Numerical Linear Algebra with Applications
Special Issue: Multigrid Methods
Volume 13, Issue 2-3, pages 251–273, March - April 2006
Additional Information
How to Cite
Limon, A. and Morris, H. (2006), A multilevel adaptive solver based on second-generation wavelet thresholding techniques. Numer. Linear Algebra Appl., 13: 251–273. doi: 10.1002/nla.479
Publication History
- Issue published online: 22 FEB 2006
- Article first published online: 2 FEB 2006
- Manuscript Accepted: 17 NOV 2005
- Manuscript Revised: 7 NOV 2005
- Manuscript Received: 16 MAY 2005
Funded by
- Claremont Graduate University
- Abstract
- References
- Cited By
Keywords:
- second-generation wavelet grid refinement;
- non-dyadic grids;
- adaptive multigrid;
- singular perturbation;
- MOSFETs;
- quantum tunnelling;
- density-gradient equation
Abstract
In this manuscript, we introduce a second-generation wavelet thresholding technique used to construct a numerically stable non-dyadic sparse grid representation. The resulting second-generation wavelet projectors, when coupled to a multigrid solver, provide an elegant method for integrating the numerical solution. The combined method is then utilized in the solution of a singular perturbation problem that arises when modelling an n-MOS gate exhibiting quantum tunnelling. The resulting solution is compared with the full Schrödinger–Poisson system, and the two solutions are shown to be in good agreement. Copyright © 2006 John Wiley & Sons, Ltd.